How to Compute Diffusion Indexes
Diffusion indexes measure the proportion of the components that
are rising. The first step in computing the diffusion indexes is to
calculate if a component increased, decreased, or had no change.
Components that rise more than 0.05 percent are given a value of 1, components
that change less than 0.05 percent are given a value of 0.5, and components
that fall more than 0.05 percent are given a value of 0. Next, sum the
values of the components. Third, divide by the number of components.
Finally, multiply by 100. NOTE: For series that are already in percent
form, such as BCI129  interest rate spread of the U.S. Leading Index, arithmetic differences are used
instead of percent changes.
Onemonth diffusion indexes measure the percent of components rising over a
onemonth span, i.e., June 1997 to July 1997. Sixmonth diffusion
indexes measure the percent of components rising over a sixmonth span, i.e.,
June 1997 to Dec. 1997.
Using data as of October 1998, the following example uses the components of
the U.S. leading index to compute a onemonth diffusion index.
Date 
BCI1 
BCI5 
BCI8 
BCI32 
BCI27 
BCI29 
BCI19 
BCI106 
BCI129 
BCI83 
Index Level 
Jun97 
41.9 
337.2 
150,729 
54.9 
44,749 
1,398 
876.29 
3,501.3 
0.93 
98.9 
Jul97 
41.9 
305.2 
151,764 
54.8 
44,873 
1,441 
925.29 
3,509.0 
0.70 
102.6 
Values for Jul97 
0.5 
1 
1 
0 
1 
1 
1 
1 
0 
1 
75 
Sum the values to obtain 7.5. Divide by 10 (the number of
components), multiply by 100 to get 75
Using this procedure, the following table shows the value for July
1997 to Dec. 1997
Date 
BCI1 
BCI5 
BCI8 
BCI32 
BCI27 
BCI29 
BCI19 
BCI106 
BCI129 
BCI83 
Index Level 
Jul97 
0.5 
1 
1 
0 
1 
1 
1 
1 
0 
1 
75 
Aug97 
0.5 
0 
1 
1 
1 
1 
1 
1 
1 
0 
75 
Sep97 
0.5 
1 
0 
0 
1 
1 
1 
1 
0 
1 
65 
Oct97 
1 
0 
0 
0 
1 
1 
1 
1 
0 
1 
60 
Nov97 
1 
0 
0 
1 
1 
0 
0 
1 
0 
0 
40 
Dec97 
1 
1 
1 
0 
0 
0 
0 
1 
0 
0 
40 
Sixmonth Diffusion Index
The sixmonth diffusion index follows the same
steps as the onemonth index with the exception that diffusion index levels
are centered within the sixmonth span. Index levels are placed in the fourth
month of the span. If we are calculating index levels for the June 1997 to
Dec. 1997 span, the diffusion index level would be place in Sept. 1997.
Using this procedure, the following table shows the values for components
for the sixmonth diffusion index from June 1997 to December 1997.
Date 
A0M001 
A0M005 
A0M008 
A0M032 
A0M027 
A0M029 
U0M019 
A0M106 
U0M129 
U0M083 
Index Level 
Jun97 
41.9 
337.2 
150,729 
54.9 
44,749 
1,398 
876.29 
3,501.3 
0.93 
98.9 
Jul97 
41.9 
305.2 
151,764 
54.8 
44,873 
1,441 
925.29 
3,509.0 
0.7 
102.6 
Aug97 
41.9 
326.2 
155,386 
55.6 
45,031 
1,445 
927.74 
3,534.1 
0.76 
100.3 
Sep97 
41.9 
310.2 
154,784 
55.5 
46,336 
1,475 
937.02 
3,548.4 
0.67 
100.7 
Oct97 
42.0 
311.1 
154,233 
55.0 
47,387 
1,502 
951.16 
3,563.5 
0.53 
102.8 
Nov97 
42.1 
318.6 
152,877 
55.2 
55,182 
1,475 
938.92 
3,583.0 
0.36 
102.3 
Dec97 
42.2 
313.4 
155,490 
54.0 
44,180 
1,467 
962.37 
3,601.7 
0.31 
96.1 
Values for Sep97 
1 
1 
1 
0 
0 
1 
1 
1 
0 
0 
60 
